Diﬀusion tensor imaging has become an important research and clinical tool, owing to its unique ability to infer microstructural properties of living tissue. Increased use has led to a demand for statistical tools to analyze diﬀusion tensor data and perform, for example, conﬁdence estimates, ROI analysis, and group comparisons. A ﬁrst step towards developing a statistical framework is establishing the basic notion of distance between tensors. We investigate the properties of two previously proposed metrics that deﬁne a Riemannian manifold: the aﬃne-invariant and Euclidean metrics. We ﬁnd that the Euclidean metric is more appropriate for intra-voxel comparisons, and suggest that a context-dependent metric may be required for inter-voxel comparisons.